Question 64421
Consider the following:
Let n = the number of the square.
For n = 1 (the first square), the number of pennies is {{{1 = 2^(n-1)}}} = {{{2^0}}} = 1
For n = 2, the number of pennies is {{{2 = 2^(n-1)}}} = {{{2^1}}} = 2
For n = 3, the number of pennies is {{{4 = 2^(n-1)}}} = {{{2^2}}} = 4
...and so on.
For the 32nd square, n = 32, so the number of pennies on this square is {{{2^(32-1) = 2^31}}} and {{{2^31 = 2147483648}}}
Change this to dollars by diving by 100 (100 pennies to the dollar) and you get:
$21,474,836.48 Just on the 32nd square.

To find the total number of pennies when all 64 squares are filled in this fashion, it's {{{2^64 - 1}}} Note here, that the 1 is subtracted after raising 2 to the 64th power. The resulting number is too large for most calculators to display, but here is the result: {{{2^64 - 1 = 18446744073709551615}}}pennies.
In dollars, that's: $184,467,440,737,095,516.15